Hmm. I figured it out. My miniscule understanding of iptables does not allow me to explain this, but if I move the rule for port 4567 up in the chain, it works. I thought they should just be going down the chain rules. Missing something here. Anyway, the issue seems to be resolved. If someone could explain why - this would be interesting to know.
Chain INPUT (policy ACCEPT 0 packets, 0 bytes)
pkts bytes target prot opt in out source destination
2590K 1747M ACCEPT all -- * * 0.0.0.0/0 0.0.0.0/0 state RELATED,ESTABLISHED
159 13356 ACCEPT icmp -- * * 0.0.0.0/0 0.0.0.0/0
222 13300 ACCEPT all -- lo * 0.0.0.0/0 0.0.0.0/0
25 1420 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:22
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:4567
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:2080
54 2736 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:443
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:1002
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:5666
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:8140
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:4545
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:5222
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:5269
574 45099 ACCEPT udp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW udp dpt:161
0 0 ACCEPT udp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW udp dpt:162
11540 1407K REJECT all -- * * 0.0.0.0/0 0.0.0.0/0 reject-with icmp-host-prohibited
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 tcp dpt:6379
0 0 ACCEPT tcp -- * * 0.0.0.0/0 0.0.0.0/0 state NEW tcp dpt:80
